1. Field of the Invention
The invention relates generally to fiberoptic rotation sensors, and especially to apparatus and methods for measuring the rotation-induced phase shift between light waves counterpropagating in the fiberoptic coil of a Sagnac interferometer to determine the rate of rotation of the coil.
2. Description of the Related Art
A fiberoptic interferometer used for rotation sensing and measurement generally comprises a coherent source of light, a multiturn optical fiber coil, means for coupling light from the source into and out of the coil, and means for detecting and processing an interference light signal coming from the coil. The interferometer "proper" frequency is defined as 1/2.tau., where .tau. is the time required for light to travel around the gyro coil.
There are two types of disturbances in an optical path that can give rise to phase shifts in light waves traveling in opposite directions around a closed optical path: reciprocal and nonreciprocal. A reciprocal disturbance is one that affects either light wave in a similar manner despite the fact that the two waves are traveling in different directions and may be subjected to the disturbance at different times. A nonreciprocal disturbance affects the two waves differently, either because it occurs over a time interval comparable to the time it takes a wave to travel around the closed path, or because the effect it has on a wave depends on the direction of propagation of the wave around the closed path.
The Sagnac effect, a relativistic phenomenon, is a nonreciprocal effect in which the rotation of a closed optical path causes light waves propagating in opposite directions along the path to take different amounts of time to complete a transit of the closed path. This difference in transit time results in a phase difference between the two light waves proportional to rotation rate. When the beams are recombined on a photodetector, they give rise to an interference pattern which is a function of the nonreciprocal phase difference or shift. Measurement of the phase difference provides a measure of the rate of rotation of the optical path.
If .DELTA..phi. denotes the Sagnac phase difference between two recombined counterpropagating light beams, the intensity of light due to the interfering beams varies as cos(.DELTA..phi.). When the phase difference is close to zero, the cosine function varies only slightly with changes in phase difference. In order to increase the sensitivity of detection, it is advantageous to introduce artificially an added fixed phase shift or "bias" to shift to a point of operation on the cosine curve where the rate of change of output intensity with respect to .DELTA..phi. is greater. In particular, maximum sensitivity and linearity of response are achieved by shifting to a point such as .pi./2. At this point, the light intensity is proportional to cos(.DELTA..phi.+.pi./2)=sin(.DELTA..phi.). The periodic nature of the cosine function results in an equivalent maximum sensitivity and linearity of response (apart from algebraic sign) at any odd integral multiple of plus or minus .pi./2.
It has proven difficult to a construct a sufficiently stable device for introducing a nonreciprocal bias. In order to obviate stability problems, various methods have been proposed for modulating the phase of the light waves propagating within the closed optical path of a Sagnac interferometer.
A phase modulator device can be based, for example, on the change in refractive index with applied voltage in an electro-optic crystal forming part of the closed optical path of the interferometer. If the phase modulator is placed near one end of the fiber coil, application of a voltage to the modulator produces a phase shift in one of the counterpropagating waves that is not experienced by the other until it has traveled all the way around the coil. There the second wave experiences a phase shift which is delayed by the length of time required for light to propagate around the coil, a time given by EQU .tau..sub.o =nL/c,
where n is the index of refraction of the fiber material, L is the length of the fiber coil, and c is the speed of light in vacuum. If V(t) is a time-varying signal applied to the phase modulator, the phase difference .phi..sub.m (t)-.phi..sub.m (t-.tau.) between the counterpropagating light waves is proportional to V(t)-V(t-.tau..sub.o). In this way a phase bias can be produced which sets the operating point of the interferometer.
If there is a rotation of the fiber coil, a phase shift .DELTA..phi. will be added to the phase bias due to the nonreciprocal nature of the Sagnac effect. Although it is possible to use the output signal of the photodetector to measure the rotation directly, it is preferable to use a "nulling" or "zeroing" method to measure the rotation indirectly, in order to avoid errors resulting from drifts in the light level dependence and to produce a linear scale factor. The idea is to generate electrically a negative feedback signal which is equal in magnitude but opposite in sign to the rotationally-induced signal, and to use the feedback signal to "null" or "zero" the rotation signal. Application of the feedback modulation signal to the phase modulator produces a phase difference between the counterpropagating waves which is continuously equal and opposite in sign compared to the phase shift induced by the rotation of the closed optical path. A method such as this in which there is a closed feedback loop is often referred to as a "closed-loop" method.
One method of phase modulation used in closed-loop methods, generally known as the "serrodyne method", generates a feedback modulation signal which is a voltage ramp signal having a slope proportional to .DELTA..phi..sub.o /.tau..sub.o, where .phi..sub.o is a constant rotationally-induced phase shift and .tau..sub.o is the time taken for a light wave to travel around the closed light path of the interferometer in the absence of any rotation. Since the phase ramp signal cannot increase indefinitely, the serrodyne method actually generates a sawtooth waveform with a peak-to-peak amplitude of 2.pi. radians, with the 2.pi. phase transition effectively resetting the operating point of the interferometer to an equivalent position on the curve relating output signal to input phase difference. A bias modulation signal consists of a voltage square-wave having an amplitude which induces a phase shift of plus or minus .pi./2 radians and a frequency equal to 1/2.tau..sub.o.
U.S. Pat. No. 4,705,399 to Graindorge et al., entitled "Device for Measuring a Nonreciprocal Phase Shift Produced in a Closed-Loop Interferometer," discloses a serrdyne phase modulation method in which a digital phase ramp in the form of a staircase-shaped voltage feedback signal is combined with a bias modulation signal consisting of a voltage square-wave having an amplitude which induces a phase shift of plus or minus .pi./2 radians and a frequency equal to 1/2.tau..sub.o. The digital staircase signal consists of a sequence of voltage steps, each of duration .tau..sub.o. In general, the amplitude of each step change is calculated to provide a nonreciprocal phase shift of plus or minus .pi./2 radians minus the Sagnac phase shift. The step sequence is generally n steps of positive voltage levels followed by n steps of negative voltage levels. The light intensity output of the interferometer fiber loop is demodulated at the bias modulation frequency or some multiple thereof, namely 1/2n.tau..sub.o, where n is a nonzero integer.
The resulting signal is proportional to the Sagnac phase shift. This signal is used in a closed-loop type of operation to continuously null the Sagnac phase shift. To avoid problems with voltage saturation, the modulation steps are occasionally required to "roll over" or start over again by the application of a step voltage signal. The step voltage applied to the phase modulator is adjusted to provide an additional phase shift of 2.pi.m radians (where m is an integer) to keep the voltage to the phase modulator in a resonable operating range. Additional demodulation logic may be employed during these roll-overs to determine the error in estimated phase modulator gain. Through subsequent roll-overs, the scale factor error or gain error may be nulled. The scale factor or gain is the proportionality constant relating the phase induced by the phase modulator in response to a given value of input voltage.
Another phase modulation method which can be used is direct digital feedback, which is also a closed-loop method. Such a method is disclosed in U.S. patent application Ser. No. 031,323, entitled "Rotation Rate Nulling Servo and Method for Fiberoptic Rotation Sensor," by Jim Steele, filed Mar. 27, 1987, and assigned to the assignee of the present invention. The application by Steele is hereby incorporated by reference into the present application.
The Steele application discloses a direct digital feedback circuit which operates by alternately presetting the voltage drive on the phase modulator to zero and waiting for at least one transit time .tau..sub.o, then switching the phase modulator voltage to a level corresponding to a nonreciprocal phase shift which is the difference between a reference (-3.pi./2, -.pi./2, +.pi./2, +3.pi./2 radians) and the Sagnac phase signal. The resulting light intensity signal is gated and observed for one transit time .tau..sub.o immediately following the setting of the reference voltage. The process is repeated in a predetermined sequence of reference levels and the results are processed to continuously develop a Sagnac phase estimate and a phase modulator scale factor or gain error (secondary control) with which to adjust the amplitudes of the voltages to the phase modulator.
The overall scale factor or gain for an open-loop interferometer is the product of the Sagnac scale factor or gain and the phase modulation scale factor or gain. The Sagnac scale factor is the constant of proportionality between rate of rotation of the closed light path and the Sagnac phase difference. The phase modulation scale factor is the constant of proportionality between the phase shift effected by the phase modulator and the input voltage to the phase modulator.
The modulation signal applied to the phase modulator in a Sagnac interferometer must provide for rate and scale factor correction signals that are derived from the detected light signal from the interferometer. Voltage signal waveforms previously utilized in phase modulation methods have detected rate at other than the proper frequency, which has led to measurement errors.